Motor vehicles can be equipped with a radar-based back-up and parking aid (BUA) such as the Dual-Beam Radar Back-Up Aid produced by Delphi Corporation for producing audible and/or visual driver alerts when an obstacle is detected in the rear travel path of the vehicle. In a typical installation, the system includes a radar sensor module mounted in a protected location behind a plastic fascia that covers the rear bumper. Although the bumper fascia protects the sensor module from physical damage and environmental contamination, it can also increase the effective level of clutter or noise detected by the sensor, particularly under conditions that cause the fascia to shift or flex. Since this and other clutter can be falsely interpreted as an obstacle and result in false target detection, the target discrimination threshold is customarily set to relatively high level for maximum noise rejection. Unfortunately, this can also unnecessarily limit the target detection sensitivity of the system because the same target discrimination threshold is used under all conditions. Accordingly, what is needed is a way of improving the target detection sensitivity without causing false target detection.